Blender game character is not responding to game logic
The BGE can't handle the Mirror Modifier when you apply it and change the order of the modifiers:



Some notes:


For performance and to avoid issues it would be better to apply the subsurf also
80 Frames is a bit long for this walk cycle
Loop Stop / End should be used in the action actuators
Related: How should an animated character be moved while repeating a walk cycle?


Result (reduced to 20 frames and adjusted movement):